Abstract: We propose a new technique for consistent estimation of the number and locations of the change-points in the second-order structure of a time series.
The core of the segmentation procedure is the Wild Binary Segmentation method (WBS), a technique which involves a certain randomised mechanism. The advantage of WBS over the standard Binary Segmentation lies in its localisation feature, thanks to which it works in cases where the spacings between change-points are short. In addition, we do not restrict the total number of change-points a time series can have. We also ameliorate the performance of our method by combining the CUSUM statistics obtained at different scales of the wavelet periodogram, our main change-point detection statistic, which allows a rigorous estimation of the local autocovariance of a piecewise-stationary process. We provide a simulation study to examine the performance of our method for different types of scenarios. A proof of consistency is also provided. Our methodology is implemented in the R package wbsts, available from CRAN.

Key words and phrases: Binary segmentation, change-points, locally stationary wavelet processes, non-stationarity.